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PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

Mass loss at the asymptotic giant branch (AGB) plays an important role not only in the final fates of stars, but also in the chemical evolution of galaxies. Nevertheless, the metallicity effects on AGB mass loss are not yet fully understood. We present spatially resolved observations of an AGB star, V3, in the metal-poor globular cluster 47 Tuc (NGC 104). The AGB star 47 Tuc V3 was observed using the GRAVITY instrument at ESO's Very Large Telescope Interferometer (VLTI) at 2-2.45 micron with a projected baseline length of up to 96 m. The object 47 Tuc V3 has been spatially resolved and stands as the first to attempt to spatially resolve an individual star in a globular cluster. The uniform-disk fit to the observed data results in an angular diameter of ~0.7 mas. Our modeling of the spectral energy distribution and near-infrared interferometric GRAVITY data suggests that the observed data can be explained by an optically thin dust shell with a 0.55 micron optical depth of 0.05-0.25, consisting of metallic iron grains, likely together with effects of the extended atmosphere of the central star. The dust temperature at the inner shell boundary is 500-800 K (corresponding to 23-90 stellar radii), significantly lower than observed in nearby oxygen-rich AGB stars. Radiation pressure on small (< 0.05 micron) iron grains is not sufficient to drive stellar winds. Therefore, iron grains may grow to larger sizes, even in the metal-poor environment. Alternatively, it is possible that the observed iron grain formation is a result of the mass outflow initiated by some other mechanism(s). The sensitivity and angular resolution of VLTI provides a new window onto spatially resolving individual stars in metal-poor globular clusters. This allows us to improve subsequent studies of the metallicity dependence of dust formation and mass loss., Comment: 7 pages, 3 figures, accepted for publication in Astronomy and Astrophysics

The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism., Comment: 5 pages

In this paper we present the first-ever $L$- and $M$-band interferometric observations of Circinus, building upon a recent $N$-band analysis. We used these observations to reconstruct images and fit Gaussian models to the $L$ and $M$ bands. Our findings reveal a thin edge-on disk whose width is marginally resolved and is the spectral continuation of the disk imaged in the $N$ band to shorter wavelengths. Additionally, we find a point-like source in the $L$ and $M$ bands that, based on the $LMN$-band spectral energy distribution fit, corresponds to the $N$-band point source. We also demonstrate that there is no trace of direct sightlines to hot dust surfaces in the circumnuclear dust structure of Circinus. By assuming the dust is present, we find that obscuration of A$_{\rm V} \gtrsim 250$ mag is necessary to reproduce the measured fluxes. Hence, the imaged disk could play the role of the obscuring "torus" in the unified scheme of active galactic nuclei. Furthermore, we explored the parameter space of the disk + hyperbolic cone radiative transfer models and identify a simple modification at the base of the cone. Adding a cluster of clumps just above the disk and inside the base of the hyperbolic cone provides a much better match to the observed temperature distribution in the central aperture. This aligns well with the radiation-driven fountain models that have recently emerged. Only the unique combination of sensitivity and spatial resolution of the VLTI allows such models to be scrutinized and constrained in detail. We plan to test the applicability of this detailed dust structure to other MATISSE-observed active galactic nuclei in the future., Comment: Main article: 12 pages, 6 figures. Accepted for publication in A&A. arXiv admin note: text overlap with arXiv:2205.01575

The notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct., Comment: 6 pages

Active galactic nuclei play a key role in the evolution of galaxies, but their inner workings and physical connection to the host are poorly understood due to a lack of angular resolution. Infrared interferometry makes it possible to resolve the circumnuclear dust in the nearby Seyfert 2 galaxy, Circinus. Previous observations have revealed complex structures and polar dust emission but interpretation was limited to simple models. MATISSE makes it possible to image these structures for the first time. We observed the Circinus Galaxy with VLTI/MATISSE, producing 150 correlated flux spectra and 100 closure phase spectra. We reconstructed images in the N-band at ~10 mas resolution. We fit blackbody functions with dust extinction to several aperture-extracted fluxes from the images to produce a temperature distribution of central dusty structures. We find significant substructure in the circumnuclear dust: central unresolved flux of ~0.5 Jy, a thin disk 1.9 pc in diameter oriented along ~45 deg,and a ~4x1.5 pc polar emission extending orthogonal to the disk. The polar emission exhibits patchiness, which we attribute to clumpy dust. Flux enhancements to the east and west of the disk are seen for the first time. We distinguish the temperature profiles of the disk and of the polar emission: the disk shows a steep temperature gradient indicative of denser material; the polar profile is flatter, indicating clumpiness and/or lower dust density. The unresolved flux is fitted with a high temperature, ~370 K. The polar dust remains warm (~200 K) out to 1.5 pc from the disk. The recovered morphology and temperature distribution resembles modeling of accretion disks with radiation-driven winds at large scales, but we placed new constraints on the subparsec dust. The subparsec features imaged here place new constraints on the physical modeling of circumnuclear dust in active galaxies., Comment: Accepted for publication in A&A

In the widely accepted 'Unified Model' solution of the classification puzzle of Active Galactic Nuclei, the orientation of a dusty accretion torus around the central black hole dominates their appearance. In 'type-1' systems, the bright nucleus is visible at the centre of a face-on torus. In 'type-2' systems the thick, nearly edge-on torus hides the central engine. Later studies suggested evolutionary effects and added dusty clumps and polar winds but left the basic picture intact. However, recent high-resolution images of the archetypal type-2 galaxy NGC 1068 suggested a more radical revision. They displayed a ring-like emission feature which the authors advocated to be hot dust surrounding the black hole at the radius where the radiation from the central engine evaporates the dust. That ring is too thin and too far tilted from edge-on to hide the central engine, and ad hoc foreground extinction is needed to explain the type-2 classification. These images quickly generated reinterpretations of the type 1-2 dichotomy. Here we present new multi-band mid-infrared images of NGC1068 that detail the dust temperature distribution and reaffirm the original model. Combined with radio data, our maps locate the central engine below the previously reported ring and obscured by a thick, nearly edge-on disk, as predicted by the Unified Model. We also identify emission from polar flows and absorbing dust that is mineralogically distinct from that towards the Milky Way centre., Comment: In press at Nature

The asymptotic giant branch (AGB) star HR3126, associated with the arcminute-scale bipolar Toby Jug Nebula, provides a rare opportunity to study the emergence of bipolar structures at the end of the AGB phase. We carried out long-baseline interferometric observations with AMBER and GRAVITY (2--2.45 micron) at the Very Large Telescope Interferometer, speckle interferometric observations with VLT/NACO (2.24 micron), and imaging with SPHERE-ZIMPOL (0.55 micron) and VISIR (7.9--19.5 micron). The images reconstructed in the continuum at 2.1--2.29 micron from the AMBER+GRAVITY data reveal the central star surrounded by an elliptical ring-like structure with a semimajor and semiminor axis of 5.3 and 3.5 mas, respectively. The ring is interpreted as the inner rim of an equatorial dust disk viewed from an inclination angle of ~50 degrees, and its axis is approximately aligned with the bipolar nebula. The disk is surprisingly compact, with an inner radius of a mere 3.5 Rstar (2 au). Our 2-D radiative transfer modeling shows that an optically thick flared disk with silicate grains as large as ~4 micron can reproduce the observed continuum images and the spectral energy distribution. The images obtained in the CO first overtone bands reveal elongated extended emission around the central star, suggesting the oblateness of the star's atmosphere or the presence of a CO gas disk inside the dust cavity. The object is unresolved with SPHERE-ZIMPOL, NACO, and VISIR. If the disk formed together with the bipolar nebula, the grain growth from sub-micron to a few microns should have taken place over the nebula's dynamical age of ~3900 yrs. The non-detection of a companion in the reconstructed images implies that either its 2.2 micron brightness is more than ~30 times lower than that of the red giant or it might have been shredded due to binary interaction., Comment: 24 pages, 14 figures, published in Astronomy and Astrophysics

We study universal enveloping Hopf algebras of Lie algebras in the category of weakly complete vector spaces over the real and complex field., Comment: v2 completely rewritten and corrected. v3 title corrected. To appear in Journal of Lie Theory

The Herbig Ae star HD 169142 is known to have a gaseous disk with a large inner hole, and also a photometrically variable inner dust component in the sub-au region. Following up our previous analysis, we further studied the temporal evolution of inner dust around HD 169142, which may provide information on the evolution from late-stage protoplanetary disks to debris disks. We used near-infrared interferometric observations obtained with VLTI/PIONIER to constrain the dust distribution at three epochs spanning six years. We also studied the photometric variability of HD 169142 using our optical-infrared observations and archival data. Our results indicate that a dust ring at ~0.3 au formed at some time between 2013 and 2018, and then faded (but did not completely disappear) by 2019. The short-term variability resembles that observed in extreme debris disks, and is likely related to short-lived dust of secondary origin, though variable shadowing from the inner ring could be an alternative interpretation. If confirmed, this is the first direct detection of secondary dust production inside a protoplanetary disk., Comment: 7 pages, 3 figures. Published in ApJ Letters

Locally compact abelian groups are classified in which the sum of any two closed subgroups is itself closed. This amounts to reproving and extending results by Yu.~N.~Mukhin from 1970. Namely we contribute a complete classification of all totally disconnected \lca\ groups with $X+Y$ closed for any closed subgroups $X$ and $Y$., Comment: 38 pages, 1 figure

The mechanism of mass loss in late evolutionary stages of low- and intermediate-mass stars is not yet well understood. Therefore, it is crucial to study the dynamics of the region within a few stellar radii, where the wind acceleration is considered to take place. We present three-dimensional diagnosis of the atmospheric dynamics of the closest asymptotic giant branch (AGB) star R Dor from the low photospheric layers to the extended outer atmosphere--for the first time for a star other than the Sun. The images reconstructed with a spatial resolution of 6.8 mas--seven times finer than the star's angular diameter of 51.2 mas in the continuum--using the AMBER instrument at the Very Large Telescope Interferometer show a large, bright region over the surface of the star and an extended atmosphere. The velocity-field maps over the star's surface and atmosphere obtained from the Mg and H2O lines near 2.3 micron forming at atmospheric heights below ~1.5 stellar radii show little systematic motion beyond the measurement uncertainty of 1.7 km/s. In marked contrast, the velocity-field map obtained from the CO first overtone lines reveals systematic outward motion at 7--15 km/s in the extended outer atmosphere at a height of ~1.8 stellar radii. Given the detection of dust formation at ~1.5 stellar radii, the strong acceleration of material between ~1.5 and 1.8 stellar radii may be caused by the radiation pressure on dust grains. However, we cannot yet exclude the possibility that the outward motion may be intermittent, caused by ballistic motion due to convection and/or pulsation., Comment: 21 pages, 11 figures, accepted for publication in The Astrophysical Journal

We study group algebras for compact groups in the category of real and complex weakly complete vector spaces. We also show that the group algebra is a quotient of the weakly complete universal enveloping algebra of the Lie algebra of the compact group. We relate this to Tannaka duality, and to functorial properties of the group algebra. We determine the structure of the group algebra in terms of the irreducible representation, both in the real and the complex case. The particular case of a compact abelian group is worked out in detail., Comment: v1, 2 appeared as an Oberwolfach Preprint. v3 considerably expanded and extended. v4 final version, to appear in Journal of Lie Theory

A weakly complete vector space over $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$ is isomorphic to $\mathbb{K}^X$ for some set $X$ algebraically and topologically. The significance of this type of topological vector spaces is illustrated by the fact that the underlying vector space of the Lie algebra of any pro-Lie group is weakly complete. In this study, weakly complete real or complex associative algebras are studied because they are necessarily projective limits of finite dimensional algebras. The group of units $A^{-1}$ of a weakly complete algebra $A$ is a pro-Lie group with the associated topological Lie algebra $A_{\rm Lie}$ of $A$ as Lie algebra and the globally defined exponential function $\exp\colon A\to A^{-1}$ as the exponential function of $A^{-1}$. With each topological group, a weakly complete group algebra $\mathbb{K}[G]$ is associated functorially so that the functor $G\mapsto \mathbb{K}[G]$ is left adjoint to $A\mapsto A^{-1}$. The group algebra $\mathbb{K}[G]$ is a weakly complete Hopf algebra. If $G$ is compact, the $\mathbb{R}[G]$ contains $G$ as the set of grouplike elements. The category of all real Hopf algebras $A$ with a compact group of grouplike elements whose linear span is dense in $A$ is shown to be equivalent to the category of compact groups. The group algebra $A=\mathbb{R}[G]$ of a compact group $G$ contains a copy of the Lie algebra $\mathcal{L}(G)$ in $A_{\rm Lie}$; it also contains a copy of the Radon measure algebra $M(G,\mathbb{R})$. The dual of the group algebra $\mathbb{R}[G]$ is the Hopf algebra ${\mathcal R}(G,\mathbb{R})$ of representative functions of $G$. The rather straightforward duality between vector spaces and weakly complete vector spaces thus becomes the basis of a duality ${\mathcal R}(G,\mathbb{R})\leftrightarrow \mathbb{R}[G]$ and thus yields a new aspect of Tannaka duality., Comment: This is version 2. Only spelling mistakes and formal flaws have been corrected. Some explanations have been added. The content of the mathematical results has not been changed

The disks around some Herbig Be stars have been observed to be more compact than the expected dust sublimation radius for such objects, with highly refractory dust grains and optically thick gas emission having been proposed as possible explanations for this phenomenon. Our aim is to search for direct evidence for the presence of hot gas inside of the expected dust sublimation radius of MWC147. By combining VLTI/AMBER spectro-interferometry (R=12,000) with CRIRES spectroscopy (R=100,000) we can both spectrally and spatially resolve the Br-gamma line-emitting gas around MWC147. Our interferometric visibility modelling of MWC147 indicates the presence of a compact continuum disk with a close to face-on orientation. We model the continuum with an inclined Gaussian, as well as a ring with a radius of 0.60mas (0.39au) which is well within the expected dust sublimation radius of 1.52au. We detect no significant change in the measured visibilities across the Br-gamma line, indicating that the line-emitting gas is located in the same region as the continuum-emitting disk. We fit our AMBER spectro-interferometry data with a kinematic model of a disk in Keplerian rotation, with both the line-emitting and continuum-emitting components of the disk originating from the same compact region close to the central star. The presence of line-emitting gas in the same region as the K-band continuum supports the interpretation that the K-band continuum traces an optically-thick gas disk. Our spatially and spectrally resolved observations of MWC147 reveal that the K-band continuum and Br-gamma emission both originate from a similar compact region, with Br-gamma emitted from the accretion disk or disk wind region and exhibiting a rotational velocity profile. We conclude that we detect the presence of a compact, gaseous accretion disk in Keplerian rotation around MWC147.

During the last two decades, the first generation of beam combiners at the Very Large Telescope Interferometer has proved the importance of optical interferometry for high-angular resolution astrophysical studies in the near- and mid-infrared. With the advent of 4-beam combiners at the VLTI, the u-v coverage per pointing increases significantly, providing an opportunity to use reconstructed images as powerful scientific tools. Therefore, interferometric imaging is already a key feature of the new generation of VLTI instruments, as well as for other interferometric facilities like CHARA and JWST. It is thus imperative to account for the current image reconstruction capabilities and their expected evolutions in the coming years. Here, we present a general overview of the current situation of optical interferometric image reconstruction with a focus on new wavelength-dependent information, highlighting its main advantages and limitations. As an Appendix we include several cookbooks describing the usage and installation of several state-of-the art image reconstruction packages. To illustrate the current capabilities of the software available to the community, we recovered chromatic images, from simulated MATISSE data, using the MCMC software SQUEEZE. With these images, we aim at showing the importance of selecting good regularization functions and their impact on the reconstruction., Comment: Accepted for publication in Experimental Astronomy as part of the topical collection: Future of Optical-infrared Interferometry in Europe

A pro-Lie group $G$ is a topological group such that $G$ is isomorphic to the projective limit of all quotient groups $G/N$ (modulo closed normal subgroups $N$) such that $G/N$ is a finite dimensional real Lie group. A topological group is almost connected if the totally disconnected factor group $G_t:= G/G_0$ of $G$ modulo the identity component $G_0$ is compact. In this case it is straightforward that each Lie group quotient $G/N$ of $G$ has finitely many components. However, in spite of a comprehensive literature on pro-Lie groups, the following theorem, proved here, was not available until now: A pro-Lie group $G$ is almost connected if each of its Lie group quotients $G/N$ has finitely many connected components. The difficulty of the proof is the verification of the completeness of $G_t$.

We present the results of the largest $L^{\prime}$ ($3.8~\mu$m) direct imaging survey for exoplanets to date, the Large Binocular Telescope Interferometer (LBTI) Exozodi Exoplanet Common Hunt (LEECH). We observed 98 stars with spectral types from B to M. Cool planets emit a larger share of their flux in $L^{\prime}$ compared to shorter wavelengths, affording LEECH an advantage in detecting low-mass, old, and cold-start giant planets. We emphasize proximity over youth in our target selection, probing physical separations smaller than other direct imaging surveys. For FGK stars, LEECH outperforms many previous studies, placing tighter constraints on the hot-start planet occurrence frequency interior to $\sim20$ au. For less luminous, cold-start planets, LEECH provides the best constraints on giant-planet frequency interior to $\sim20$ au around FGK stars. Direct imaging survey results depend sensitively on both the choice of evolutionary model (e.g., hot- or cold-start) and assumptions (explicit or implicit) about the shape of the underlying planet distribution, in particular its radial extent. Artificially low limits on the planet occurrence frequency can be derived when the shape of the planet distribution is assumed to extend to very large separations, well beyond typical protoplanetary dust-disk radii ($\lesssim50$ au), and when hot-start models are used exclusively. We place a conservative upper limit on the planet occurrence frequency using cold-start models and planetary population distributions that do not extend beyond typical protoplanetary dust-disk radii. We find that $\lesssim90\%$ of FGK systems can host a 7 to 10 $M_{\mathrm{Jup}}$ planet from 5 to 50 au. This limit leaves open the possibility that planets in this range are common., Comment: 31 pages, 13 figures, accepted to AJ

We present near-infrared AMBER (R = 12, 000) and CRIRES (R = 100, 000) observations of the Herbig B[e] star MWC297 in the hydrogen Br-gamma-line. Using the VLTI unit telescopes, we obtained a uv-coverage suitable for aperture synthesis imaging. We interpret our velocity-resolved images as well as the derived two-dimensional photocenter displacement vectors, and fit kinematic models to our visibility and phase data in order to constrain the gas velocity field on sub-AU scales. The measured continuum visibilities constrain the orientation of the near-infrared-emitting dust disk, where we determine that the disk major axis is oriented along a position angle of 99.6 +/- 4.8 degrees. The near-infrared continuum emission is 3.6 times more compact than the expected dust-sublimation radius, possibly indicating the presence of highly refractory dust grains or optically thick gas emission in the inner disk. Our velocity-resolved channel maps and moment maps reveal the motion of the Br-gamma-emitting gas in six velocity channels, marking the first time that kinematic effects in the sub-AU inner regions of a protoplanetary disk could be directly imaged. We find a rotation-dominated velocity field, where the blue- and red-shifted emissions are displaced along a position angle of 24 +/- 3 degrees and the approaching part of the disk is offset west of the star. The visibility drop in the line as well as the strong non-zero phase signals can be modeled reasonably well assuming a Keplerian velocity field, although this model is not able to explain the 3 sigma difference that we measure between the position angle of the line photocenters and the position angle of the dust disk. We find that the fit can be improved by adding an outflowing component to the velocity field, as inspired by a magneto-centrifugal disk-wind scenario., Comment: 15 pages, 13 Figures

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its close connections to prime number theory are discussed and elucidated by graph theoretical tools. These investigations require a thorough reviewing and extension to present circumstances of various aspects of the general theory of locally compact groups such as -the Chabauty space of closed subgroups with its natural compact Hausdorff topology, -a very general Sylow subgroup theory for periodic groups including their Hall systems, -the scalar automorphisms of locally compact abelian groups, -the theory of products of closed subgroups and their relation to semidirect products, and -inductively monothetic groups are introduced and classified. As applications, firstly, a complete classification is given of locally compact topologically quasihamiltonian groups, which has been initiated by F. K\"ummich, and, secondly, Yu. Mukhin's classification of locally compact topologically modular groups is retrieved and further illuminated., Comment: 32 pages

High-mass multiples might form via fragmentation of self-gravitational disks or alternative scenarios such as disk-assisted capture. However, only few observational constraints exist on the architecture and disk structure of high-mass protobinaries and their accretion properties. Here we report the discovery of a close ($57.9\pm0.2$mas=170au) high-mass protobinary, IRAS17216-3801, where our VLTI/GRAVITY+AMBER near-infrared interferometry allows us to image the circumstellar disks around the individual components with 3 milliarcsecond resolution. We estimate the component masses to $\sim20$ and $\sim18 M_{\odot}$ and find that the radial intensity profiles can be reproduced with an irradiated disk model, where the inner regions are excavated of dust, likely tracing the dust sublimation region in these disks. The circumstellar disks are strongly misaligned with respect to the binary separation vector, which indicates that the tidal forces did not have time to realign the disks, pointing towards a young dynamical age of the system. We constrain the distribution of the Br$\gamma$ and CO-emitting gas using VLTI/GRAVITY spectro-interferometry and VLT/CRIRES spectro-astrometry and find that the secondary is accreting at a higher rate than the primary. VLT/NACO imaging shows $L'$-band emission on 3-4 times larger scales than the binary separation, matching the expected dynamical truncation radius for the circumbinary disk. The IRAS17216-3801 system is $\sim3\times$ more massive and $\sim5\times$ more compact than other high-mass multiplies imaged at infrared wavelengths and the first high-mass protobinary system where circumstellar and circumbinary dust disks could be spatially resolved. This opens exciting new opportunities for studying star-disk interactions and the role of multiplicity in high-mass star formation., Comment: 9 pages, 4 figures, accepted for publication in The Astrophysical Journal Letters

We are concerned with questions of the following type. Suppose that $G$ and $K$ are topological groups belonging to a certain class $\cal K$ of spaces, and suppose that $\phi:K \to G$ is an abstract (i.e. not necessarily continuous) surjective group homomorphism. Under what conditions on the group $G$ and the kernel is the homomorphism $\phi$ automatically continuous and open? Questions of this type have a long history and were studied in particular for the case that $G$ and $K$ are Lie groups, compact groups, or Polish groups. We develop an axiomatic approach, which allows us to resolve the question uniformly for different classes of topological groups. In this way we are able to extend the classical results about automatic continuity to a much more general setting., Comment: Several corrections in v2. Two references added in v3. To appear in Transformation Groups

Our recent visible polarimetric images of the well-studied AGB star W Hya taken at pre-maximum light (phase 0.92) with VLT/SPHERE-ZIMPOL have revealed clumpy dust clouds close to the star at ~2 Rstar. We present second-epoch SPHERE-ZIMPOL observations of W Hya at minimum light (phase 0.54) in the continuum (645, 748, and 820 nm), in the Halpha line (656.3 nm), and in the TiO band (717 nm) as well as high-spectral resolution long-baseline interferometric observations in 2.3 micron CO lines with the AMBER instrument at the Very Large Telescope Interferometer (VLTI). The high-spatial resolution polarimetric images have allowed us to detect clear time variations in the clumpy dust clouds as close as 34--50~mas (1.4--2.0 Rstar) to the star. We detected the formation of a new dust cloud and the disappearance of one of the dust clouds detected at the first epoch. The Halpha and TiO emission extends to ~150 mas (~6 Rstar), and the Halpha images reveal time variations. The degree of linear polarization is higher at minimum light (13--18%) than that at pre-maximum light. The power-law-type limb-darkened disk fit to the AMBER data in the continuum results in a limb-darkened disk diameter of 49.1+/-1.5 mas and a limb-darkening parameter of 1.16+/-0.49, indicating that the atmosphere is more extended with weaker limb-darkening compared to pre-maximum light. Our Monte Carlo radiative transfer modeling suggests the predominance of small (0.1 micron) grains of Al2O3, Mg2SiO4, and MgSiO3 at minimum light, in marked contrast to the predominance of large (0.5 micron) grains at pre-maximum light. The variability phase dependence of the grain size implies that small grains might just have started to form at minimum light in the wake of a shock, while the pre-maximum light phase might have corresponded to the phase of efficient grain growth., Comment: 14 pages, 9 figures, accepted for publication in Astronomy and Astrophysics

Let $G$ be a locally compact topological group, $G_0$ the connected component of its identity element, and comp(G) the union of all compact subgroups. A topological group will be called inductively monothetic if any subgroup generated (as a topological group) by finitely many elements is generated (as a topological group) by a single element. The space SUB(G) of all closed subgroups of $G$ carries a compact Hausdorff topology called the Chabauty topology. Let $F_1(G)$, respectively, $R_1(G)$, denote the subspace of all discrete subgroups isomorphic to $\mathbb Z$, respectively, all subgroups isomorphic to $\mathbb R$. It is shown that a necessary and sufficient condition for $G\in\overline{F_1(G)}$ to hold is that $G$ is abelian, and either that $G\cong \mathbb R\times {\rm comp}(G)$ and $G/G_0$ is inductively monothetic, or else that $G$ is discrete and isomorphic to a subgroup of $\mathbb Q$. It is further shown that a necessary and sufficient condition for $G\in\overline{R_1(G)}$ to hold is that $G\cong\mathbb R\times C$ for a compact connected abelian group $C$.

We present visible polarimetric imaging observations of the well-studied AGB star W Hya taken with VLT/SPHERE-ZIMPOL as well as high spectral resolution long-baseline interferometric observations with the AMBER instrument of the Very Large Telescope Interferometer (VLTI). We observed W Hya with VLT/SPHERE-ZIMPOL at three wavelengths in the continuum (645, 748, and 820 nm), in the Halpha line at 656.3 nm, and in the TiO band at 717 nm. The VLTI/AMBER observations were carried out in the wavelength region of the CO first overtone lines near 2.3 micron with a spectral resolution of 12000. Taking advantage of the polarimetric imaging capability of SPHERE-ZIMPOL combined with the superb adaptive optics performance, we have succeeded in spatially resolving three clumpy dust clouds located at ~50 mas (~2 Rstar) from the central star, revealing dust formation very close to the star. The AMBER data in the individual CO lines suggest a molecular outer atmosphere extending to ~3 Rstar. Furthermore, the SPHERE-ZIMPOL image taken over the Halpha line shows emission with a radius of up to ~160 mas (~7 Rstar). We found that dust, molecular gas, and Halpha-emitting hot gas are coexisting within 2--3 Rstar. Our modeling suggests that the observed polarized intensity maps can reasonably be explained by large (0.4--0.5 micron) grains of Al2O3 or Mg2SiO4 or MgSiO3 in an optically thin shell with an inner boundary radius of 1.9--2.0 Rstar. The observed clumpy structure can be reproduced by a density enhancement by a factor of 4 +/- 1. The grain size derived from our polarimetric images is consistent with the prediction of the hydrodynamical models for the mass loss driven by the scattering due to micron-sized grains. The detection of the clumpy dust clouds close to the star lends support to the dust formation induced by pulsation and large convective cells as predicted by the 3-D simulations for AGB stars., Comment: 12 pages, 9 figures, accepted for publication in Astronomy and Astrophysics, short discussion of non-equilibrium gas-dust chemistry models added

As gas giant planets and brown dwarfs radiate away the residual heat from their formation, they cool through a spectral type transition from L to T, which encompasses the dissipation of cloud opacity and the appearance of strong methane absorption. While there are hundreds of known T-type brown dwarfs, the first generation of directly-imaged exoplanets were all L-type. Recently, Kuzuhara et al. (2013) announced the discovery of GJ 504 b, the first T dwarf exoplanet. GJ 504 b provides a unique opportunity to study the atmosphere of a new type of exoplanet with a ~500 K temperature that bridges the gap between the first directly imaged planets (~1000 K) and our own Solar System's Jupiter (~130 K). We observed GJ 504 b in three narrow L-band filters (3.71, 3.88, and 4.00 microns), spanning the red end of the broad methane fundamental absorption feature (3.3 microns) as part of the LEECH exoplanet imaging survey. By comparing our new photometry and literature photometry to a grid of custom model atmospheres, we were able to fit GJ 504 b's unusual spectral energy distribution for the first time. We find that GJ 504 b is well-fit by models with the following parameters: T_eff=544+/-10 K, g<600 m/s^2, [M/H]=0.60+/-0.12, cloud opacity parameter of f_sed=2-5, R=0.96+/-0.07 R_Jup, and log(L)=-6.13+/-0.03 L_Sun, implying a hot start mass of 3-30 M_jup for a conservative age range of 0.1-6.5 Gyr. Of particular interest, our model fits suggest that GJ 504 b has a super-stellar metallicity. Since planet formation can create objects with non-stellar metallicities, while binary star formation cannot, this result suggests that GJ 504 b formed like a planet, not like a binary companion., Comment: resubmitted to ApJ with referee's comments

We present high-resolution Large Binocular Telescope LBTI/LMIRcam images of the spectroscopic and astrometric binary NO UMa obtained as part of the LBTI Exozodi Exoplanet Common Hunt (LEECH) exoplanet imaging survey. Our H, K$_s$, and L'-band observations resolve the system at angular separations <0.09". The components exhibit significant orbital motion over a span of ~7 months. We combine our imaging data with archival images, published speckle interferometry measurements, and existing spectroscopic velocity data to solve the full orbital solution and estimate component masses. The masses of the K2.0$\pm$0.5 primary and K6.5$\pm$0.5 secondary are 0.83$\pm$0.02 M$_{\odot}$ and 0.64$\pm$0.02 M$_{\odot}$, respectively. We also derive a system distance of d = 25.87$\pm$0.02 pc and revise the Galactic kinematics of NO UMa. Our revised Galactic kinematics confirm NO UMa as a nuclear member of the ~500 Myr old Ursa Major moving group and it is thus a mass and age benchmark. We compare the masses of the NO UMa binary components to those predicted by five sets of stellar evolution models at the age of the Ursa Major group. We find excellent agreement between our measured masses and model predictions with little systematic scatter between the models. NO UMa joins the short list of nearby, bright, late-type binaries having known ages and fully characterized orbits., Comment: 11 pages, 5 figures, 4 tables, accepted for publication in ApJ

The red giant L2 Pup started a dimming event in 1994, which is considered to be caused by the ejection of dust clouds. We present near-IR aperture-synthesis imaging of L2 Pup achieved by combining data from VLT/NACO speckle observations and long-baseline interferometric observations with the AMBER instrument of the Very Large Telescope Interferometer (VLTI). We also extracted an 8.7 micron image from the mid-IR VLTI instrument MIDI. Our aim is to spatially resolve the innermost region of the circumstellar environment. The diffraction-limited image at 2.27 micron obtained by bispectrum speckle interferometry with NACO with a spatial resolution of 57 mas shows an elongated component. The aperture-synthesis imaging combining the NACO speckle data and AMBER data (2.2--2.29 micron) with a spatial resolution of 5.6x7.3 mas further resolves not only this elongated component, but also the central star. The reconstructed image reveals that the elongated component is a nearly edge-on disk with a size of ~180x50 mas lying in the E-W direction, and furthermore, that the southern hemisphere of the central star is severely obscured by the equatorial dust lane of the disk. The angular size of the disk is consistent with the distance that the dust clouds that were ejected at the onset of the dimming event should have traveled by the time of our observations, if we assume that the dust clouds moved radially. This implies that the formation of the disk may be responsible for the dimming event. The 8.7 micron image with a spatial resolution of 220 mas extracted from the MIDI data taken in 2004 (seven years before the AMBER and NACO observations) shows an approximately spherical envelope without a signature of the disk. This suggests that the mass loss before the dimming event may have been spherical., Comment: 11 pages, 11 figures, accepted for publication in Astronomy and Astrophysics

A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally compact group which has a compact quotient group modulo its identity component and thus, in particular, each compact and each connected locally compact group; it also includes all locally compact abelian groups. This paper provides an overview of the structure theory and Lie theory of pro-Lie groups including results more recent than those in the authors' reference book on pro-Lie groups. Significantly, it also includes a review of the recent insight that weakly complete unital algebras provide a natural habitat for both pro-Lie algebras and pro-Lie groups, indeed for the exponential function which links the two. (A topological vector space is weakly complete if it is isomorphic to a power $\R^X$ of an arbitrary set of copies of $\R$. This class of real vector spaces is at the basis of the Lie theory of pro-Lie groups.) The article also lists 12 open questions connected with pro-Lie groups., Comment: 19 pages

Accretion and ejection are tightly connected and represent the fundamental mechanisms regulating star formation. However, the exact physical processes involved are not yet fully understood. We present high angular and spectral resolution observations of the Br Gamma emitting region in the Herbig Ae star HD163296 (MWC275) in order to probe the origin of this line and constrain the physical processes taking place at sub-AU scales in the circumstellar region. By means of VLTI-AMBER observations at high spectral resolution (R~12000), we studied interferometric visibilities, wavelength-differential phases, and closure phases across the Br Gamma line of HD163296. To constrain the physical origin of the Br Gamma line in Herbig Ae stars, all the interferometric observables were compared with the predictions of a line radiative transfer disc wind model. The measured visibilities clearly increase within the Br Gamma line, indicating that the Br Gamma emitting region is more compact than the continuum. By fitting a geometric Gaussian model to the continuum-corrected Br Gamma visibilities, we derived a compact radius of the Br Gamma emitting region of ~0.07+/-0.02AU (Gaussian half width at half maximum; or a ring-fit radius of ~0.08+/-0.02AU). To interpret the observations, we developed a magneto-centrifugally driven disc wind model. Our best disc wind model is able to reproduce, within the errors, all the interferometric observables and it predicts a launching region with an outer radius of ~0.04AU. However, the intensity distribution of the entire disc wind emitting region extends up to ~0.16AU. Our observations, along with a detailed modelling of the Br Gamma emitting region, suggest that most of the Br Gamma emission in HD163296 originates from a disc wind with a launching region that is over five times more compact than previous estimates of the continuum dust rim radius., Comment: Accepted for publication in A&A

In Spring 2013, the LEECH (LBTI Exozodi Exoplanet Common Hunt) survey began its $\sim$130-night campaign from the Large Binocular Telescope (LBT) atop Mt Graham, Arizona. This survey benefits from the many technological achievements of the LBT, including two 8.4-meter mirrors on a single fixed mount, dual adaptive secondary mirrors for high Strehl performance, and a cold beam combiner to dramatically reduce the telescope's overall background emissivity. LEECH neatly complements other high-contrast planet imaging efforts by observing stars at L' (3.8 $\mu$m), as opposed to the shorter wavelength near-infrared bands (1-2.4 $\mu$m) of other surveys. This portion of the spectrum offers deep mass sensitivity, especially around nearby adolescent ($\sim$0.1-1 Gyr) stars. LEECH's contrast is competitive with other extreme adaptive optics systems, while providing an alternative survey strategy. Additionally, LEECH is characterizing known exoplanetary systems with observations from 3-5$\mu$m in preparation for JWST., Comment: 12 pages, 5 figures. Proceedings of the SPIE, 9148-20

In 1985 S.~Saeki and K.~Stromberg published the following question: {\it Does every infinite compact group have a subgroup which is not Haar measurable?} An affirmative answer is given for all compact groups with the exception of some metric profinite groups known as strongly complete. In this spirit it is also shown that every compact group contains a non-Borel subgroup.

In February 2013, the LEECH (LBTI Exozodi Exoplanet Common Hunt) survey began its 100-night campaign from the Large Binocular Telescope atop Mount Graham in Arizona. LEECH nearly complements other high-contrast planet imaging efforts by observing stars in L' band (3.8 microns) as opposed to the shorter wavelength near-infrared bands (1-2.3 microns). This part of the spectrum offers deeper mass sensitivity for intermediate age (several hundred Myr-old) systems, since their Jovian-mass planets radiate predominantly in the mid-infrared. In this proceedings, we present the science goals for LEECH and a preliminary contrast curve from some early data., Comment: IAUS 299 Proceedings

We present high spectral resolution aperture-synthesis imaging of the red supergiant Antares (alpha Sco) in individual CO first overtone lines with VLTI/AMBER. The reconstructed images reveal that the star appears differently in the blue wing, line center, and red wing and shows an asymmetrically extended component. The appearance of the star within the CO lines changes drastically within one year, implying a significant change in the velocity field in the atmosphere. Our modeling suggests an outer atmosphere (MOLsphere) extending to 1.2--1.4 stellar radii with CO column densities of (0.5--1)x10^{20} cm^{-2} and a temperature of ~2000 K. While the velocity field in 2009 is characterized by strong upwelling motions at 20--30 km/s, it changed to strong downdrafts in 2010. On the other hand, the AMBER data in the continuum show only a slight deviation from limb-darkened disks and only marginal time variations. We derive a limb-darkened disk diameter of 37.38+/-0.06 mas and a power-law-type limb-darkening parameter of (8.7+/-1.6)x10^{-2} (2009) and 37.31+/-0.09 mas and (1.5+/-0.2)x10^{-1} (2010). We also obtain Teff = 3660+/-120 K and log L/Lsun = 4.88+/-0.23, which suggests a mass of 15+/-5 Msun with an age of 11-15 Myr. This age is consistent with the recently estimated age for the Upper Scorpius OB association. The properties of the outer atmosphere of Antares are similar to those of another well-studied red supergiant, Betelgeuse. The density of the extended outer atmosphere of Antares and Betelgeuse is higher than predicted by the current 3-D convection simulations by at least six orders of magnitude, implying that convection alone cannot explain the formation of the extended outer atmosphere., Comment: 18 pages, 16 figures, accepted for publication in Astronomy and Astrophysics, short discussion on the age of Antares and the Upper Scorpius OB association added, movies of the reconstructed images available at http://www.mpifr-bonn.mpg.de/staff/kohnaka/

Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group., Comment: Minor corrections in v2 an in v3. The proof of Lemma 3.4 was incorrect in v1 - v3. A correct proof is now given in a separate erratum at the end of the article. Both the article and the erratum will appear in Crelle Journal Reine Angew. Mathematik

We present the results of the fifth Interferometric Imaging Beauty Contest. The contest consists in blind imaging of test data sets derived from model sources and distributed in the OIFITS format. Two scenarios of imaging with CHARA/MIRC-6T were offered for reconstruction: imaging a T Tauri disc and imaging a spotted red supergiant. There were eight different teams competing this time: Monnier with the software package MACIM; Hofmann, Schertl and Weigelt with IRS; Thi\'ebaut and Soulez with MiRA ; Young with BSMEM; Mary and Vannier with MIROIRS; Millour and Vannier with independent BSMEM and MiRA entries; Rengaswamy with an original method; and Elias with the radio-astronomy package CASA. The contest model images, the data delivered to the contestants and the rules are described as well as the results of the image reconstruction obtained by each method. These results are discussed as well as the strengths and limitations of each algorithm.

V921 Scorpii is a close binary system (separation 0.025") showing the B[e]-phenomenon. The system is surrounded by an enigmatic bipolar nebula, which might have been shaped by episodic mass-loss events, possibly triggered by dynamical interactions between the companion and the circumprimary disk (Kraus et al. 2012a). In this paper, we investigate the spatial structure and kinematics of the circumprimary disk, with the aim to obtain new insights into the still strongly debated evolutionary stage. For this purpose, we combine, for the first time, infrared spectro-interferometry (VLTI/AMBER, R=12,000) and spectro-astrometry (VLT/CRIRES, R=100,000), which allows us to study the AU-scale distribution of circumstellar gas and dust with an unprecedented velocity resolution of 3 km*s^-1. Using a model-independent photocenter analysis technique, we find that the Br-gamma-line emission rotates in the same plane as the dust disk. We can reproduce the wavelength-differential visibilities and phases and the double-peaked line profile using a Keplerian-rotating disk model. The derived mass of the central star is 5.4+/-0.4 M_sun*(d/1150 pc), which is considerably lower than expected from the spectral classification, suggesting that V921 Sco might be more distant (d approx 2kpc) than commonly assumed. Using the geometric information provided by our Br-gamma spectro-interferometric data and Paschen, Brackett, and Pfund line decrement measurements in 61 hydrogen recombination line transitions, we derive the density of the line-emitting gas (N_e=2...6*10^19 m^-3). Given that our measurements can be reproduced with a Keplerian velocity field without outflowing velocity component and the non-detection of age-indicating spectroscopic diagnostics, our study provides new evidence for the pre-main-sequence nature of V921 Sco., Comment: 17 pages, 11 figures, 3 tables, accepted by ApJ

We study the sub-AU-scale circumstellar environment of the Herbig Ae star HD144432 with near-infrared (NIR) VLTI/AMBER observations to investigate the structure of its inner dust disk. The interferometric observations were carried out with the AMBER instrument in the H and K band. We interpret the measured H- and K-band visibilities, the near- and mid-infrared visibilities from the literature, and the SED of HD144432 by using geometric ring models and ring-shaped temperature-gradient disk models with power-law temperature distributions. We derived a K-band ring-fit radius of 0.17 \pm 0.01 AU and an H-band radius of 0.18 \pm 0.01 AU (for a distance of 145 pc). This measured K-band radius of \sim0.17 AU lies in the range between the dust sublimation radius of \sim0.13 AU (predicted for a dust sublimation temperature of 1500 K and gray dust) and the prediction of models including backwarming (\sim0.27 AU). We found that an additional extended halo component is required in both the geometric and temperature-gradient modeling. In the best temperature- gradient model, the disk consists of two components. The inner part of the disk is a thin ring with an inner radius of \sim0.21 AU, a temperature of \sim1600 K, and a ring thickness \sim0.02 AU. The outer part extends from \sim1 AU to \sim10 AU with an inner temperature of \sim400 K. We find that the disk is nearly face-on with an inclination angle of < 28 degree. Our temperature-gradient modeling suggests that the NIR excess is dominated by emission from a narrow, bright rim located at the dust sublimation radius, while an extended halo component contributes \sim6% to the total flux at 2 {\mu}m. The MIR model emission has a two-component structure with \sim20% flux from the inner ring and the rest from the outer part. This two-component structure suggests a disk gap, which is possibly caused by the shadow of a puffed-up inner rim., Comment: 7 pages, 5 figures, accepted by A&A

Let $G$ be an infinite locally compact group and $\aleph$ a cardinal satisfying $\aleph_0\le\aleph\le w(G)$ for the weight $w(G)$ of $G$. It is shown that there is a closed subgroup $N$ of $G$ with $w(N)=\aleph$. Sample consequences are: (1) Every infinite compact group contains an infinite closed metric subgroup. (2) For a locally compact group $G$ and $\aleph$ a cardinal satisfying $\aleph_0\le\aleph\le \lw(G)$, where $\lw(G)$ is the local weight of $G$, there are either no infinite compact subgroups at all or there is a compact subgroup $N$ of $G$ with $w(N)=\aleph$. (3) For an infinite abelian group $G$ there exists a properly ascending family of locally quasiconvex group topologies on $G$, say, $(\tau_\aleph)_{\aleph_0\le \aleph\le \card(G)}$, such that $(G,\tau_\aleph)\hat{\phantom{m}}\cong\hat G$. Items (2) and (3) are shown in Section 5.